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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math.ode.nonstiff;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math.util.FastMath;<a name="line.20"></a>
<FONT color="green">021</FONT>    <a name="line.21"></a>
<FONT color="green">022</FONT>    <a name="line.22"></a>
<FONT color="green">023</FONT>    /**<a name="line.23"></a>
<FONT color="green">024</FONT>     * This class implements the 8(5,3) Dormand-Prince integrator for Ordinary<a name="line.24"></a>
<FONT color="green">025</FONT>     * Differential Equations.<a name="line.25"></a>
<FONT color="green">026</FONT>     *<a name="line.26"></a>
<FONT color="green">027</FONT>     * &lt;p&gt;This integrator is an embedded Runge-Kutta integrator<a name="line.27"></a>
<FONT color="green">028</FONT>     * of order 8(5,3) used in local extrapolation mode (i.e. the solution<a name="line.28"></a>
<FONT color="green">029</FONT>     * is computed using the high order formula) with stepsize control<a name="line.29"></a>
<FONT color="green">030</FONT>     * (and automatic step initialization) and continuous output. This<a name="line.30"></a>
<FONT color="green">031</FONT>     * method uses 12 functions evaluations per step for integration and 4<a name="line.31"></a>
<FONT color="green">032</FONT>     * evaluations for interpolation. However, since the first<a name="line.32"></a>
<FONT color="green">033</FONT>     * interpolation evaluation is the same as the first integration<a name="line.33"></a>
<FONT color="green">034</FONT>     * evaluation of the next step, we have included it in the integrator<a name="line.34"></a>
<FONT color="green">035</FONT>     * rather than in the interpolator and specified the method was an<a name="line.35"></a>
<FONT color="green">036</FONT>     * &lt;i&gt;fsal&lt;/i&gt;. Hence, despite we have 13 stages here, the cost is<a name="line.36"></a>
<FONT color="green">037</FONT>     * really 12 evaluations per step even if no interpolation is done,<a name="line.37"></a>
<FONT color="green">038</FONT>     * and the overcost of interpolation is only 3 evaluations.&lt;/p&gt;<a name="line.38"></a>
<FONT color="green">039</FONT>     *<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;p&gt;This method is based on an 8(6) method by Dormand and Prince<a name="line.40"></a>
<FONT color="green">041</FONT>     * (i.e. order 8 for the integration and order 6 for error estimation)<a name="line.41"></a>
<FONT color="green">042</FONT>     * modified by Hairer and Wanner to use a 5th order error estimator<a name="line.42"></a>
<FONT color="green">043</FONT>     * with 3rd order correction. This modification was introduced because<a name="line.43"></a>
<FONT color="green">044</FONT>     * the original method failed in some cases (wrong steps can be<a name="line.44"></a>
<FONT color="green">045</FONT>     * accepted when step size is too large, for example in the<a name="line.45"></a>
<FONT color="green">046</FONT>     * Brusselator problem) and also had &lt;i&gt;severe difficulties when<a name="line.46"></a>
<FONT color="green">047</FONT>     * applied to problems with discontinuities&lt;/i&gt;. This modification is<a name="line.47"></a>
<FONT color="green">048</FONT>     * explained in the second edition of the first volume (Nonstiff<a name="line.48"></a>
<FONT color="green">049</FONT>     * Problems) of the reference book by Hairer, Norsett and Wanner:<a name="line.49"></a>
<FONT color="green">050</FONT>     * &lt;i&gt;Solving Ordinary Differential Equations&lt;/i&gt; (Springer-Verlag,<a name="line.50"></a>
<FONT color="green">051</FONT>     * ISBN 3-540-56670-8).&lt;/p&gt;<a name="line.51"></a>
<FONT color="green">052</FONT>     *<a name="line.52"></a>
<FONT color="green">053</FONT>     * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 ao??t 2010) $<a name="line.53"></a>
<FONT color="green">054</FONT>     * @since 1.2<a name="line.54"></a>
<FONT color="green">055</FONT>     */<a name="line.55"></a>
<FONT color="green">056</FONT>    <a name="line.56"></a>
<FONT color="green">057</FONT>    public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {<a name="line.57"></a>
<FONT color="green">058</FONT>    <a name="line.58"></a>
<FONT color="green">059</FONT>      /** Integrator method name. */<a name="line.59"></a>
<FONT color="green">060</FONT>      private static final String METHOD_NAME = "Dormand-Prince 8 (5, 3)";<a name="line.60"></a>
<FONT color="green">061</FONT>    <a name="line.61"></a>
<FONT color="green">062</FONT>      /** Time steps Butcher array. */<a name="line.62"></a>
<FONT color="green">063</FONT>      private static final double[] STATIC_C = {<a name="line.63"></a>
<FONT color="green">064</FONT>        (12.0 - 2.0 * FastMath.sqrt(6.0)) / 135.0, (6.0 - FastMath.sqrt(6.0)) / 45.0, (6.0 - FastMath.sqrt(6.0)) / 30.0,<a name="line.64"></a>
<FONT color="green">065</FONT>        (6.0 + FastMath.sqrt(6.0)) / 30.0, 1.0/3.0, 1.0/4.0, 4.0/13.0, 127.0/195.0, 3.0/5.0,<a name="line.65"></a>
<FONT color="green">066</FONT>        6.0/7.0, 1.0, 1.0<a name="line.66"></a>
<FONT color="green">067</FONT>      };<a name="line.67"></a>
<FONT color="green">068</FONT>    <a name="line.68"></a>
<FONT color="green">069</FONT>      /** Internal weights Butcher array. */<a name="line.69"></a>
<FONT color="green">070</FONT>      private static final double[][] STATIC_A = {<a name="line.70"></a>
<FONT color="green">071</FONT>    <a name="line.71"></a>
<FONT color="green">072</FONT>        // k2<a name="line.72"></a>
<FONT color="green">073</FONT>        {(12.0 - 2.0 * FastMath.sqrt(6.0)) / 135.0},<a name="line.73"></a>
<FONT color="green">074</FONT>    <a name="line.74"></a>
<FONT color="green">075</FONT>        // k3<a name="line.75"></a>
<FONT color="green">076</FONT>        {(6.0 - FastMath.sqrt(6.0)) / 180.0, (6.0 - FastMath.sqrt(6.0)) / 60.0},<a name="line.76"></a>
<FONT color="green">077</FONT>    <a name="line.77"></a>
<FONT color="green">078</FONT>        // k4<a name="line.78"></a>
<FONT color="green">079</FONT>        {(6.0 - FastMath.sqrt(6.0)) / 120.0, 0.0, (6.0 - FastMath.sqrt(6.0)) / 40.0},<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>        // k5<a name="line.81"></a>
<FONT color="green">082</FONT>        {(462.0 + 107.0 * FastMath.sqrt(6.0)) / 3000.0, 0.0,<a name="line.82"></a>
<FONT color="green">083</FONT>         (-402.0 - 197.0 * FastMath.sqrt(6.0)) / 1000.0, (168.0 + 73.0 * FastMath.sqrt(6.0)) / 375.0},<a name="line.83"></a>
<FONT color="green">084</FONT>    <a name="line.84"></a>
<FONT color="green">085</FONT>        // k6<a name="line.85"></a>
<FONT color="green">086</FONT>        {1.0 / 27.0, 0.0, 0.0, (16.0 + FastMath.sqrt(6.0)) / 108.0, (16.0 - FastMath.sqrt(6.0)) / 108.0},<a name="line.86"></a>
<FONT color="green">087</FONT>    <a name="line.87"></a>
<FONT color="green">088</FONT>        // k7<a name="line.88"></a>
<FONT color="green">089</FONT>        {19.0 / 512.0, 0.0, 0.0, (118.0 + 23.0 * FastMath.sqrt(6.0)) / 1024.0,<a name="line.89"></a>
<FONT color="green">090</FONT>         (118.0 - 23.0 * FastMath.sqrt(6.0)) / 1024.0, -9.0 / 512.0},<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>        // k8<a name="line.92"></a>
<FONT color="green">093</FONT>        {13772.0 / 371293.0, 0.0, 0.0, (51544.0 + 4784.0 * FastMath.sqrt(6.0)) / 371293.0,<a name="line.93"></a>
<FONT color="green">094</FONT>         (51544.0 - 4784.0 * FastMath.sqrt(6.0)) / 371293.0, -5688.0 / 371293.0, 3072.0 / 371293.0},<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        // k9<a name="line.96"></a>
<FONT color="green">097</FONT>        {58656157643.0 / 93983540625.0, 0.0, 0.0,<a name="line.97"></a>
<FONT color="green">098</FONT>         (-1324889724104.0 - 318801444819.0 * FastMath.sqrt(6.0)) / 626556937500.0,<a name="line.98"></a>
<FONT color="green">099</FONT>         (-1324889724104.0 + 318801444819.0 * FastMath.sqrt(6.0)) / 626556937500.0,<a name="line.99"></a>
<FONT color="green">100</FONT>         96044563816.0 / 3480871875.0, 5682451879168.0 / 281950621875.0,<a name="line.100"></a>
<FONT color="green">101</FONT>         -165125654.0 / 3796875.0},<a name="line.101"></a>
<FONT color="green">102</FONT>    <a name="line.102"></a>
<FONT color="green">103</FONT>        // k10<a name="line.103"></a>
<FONT color="green">104</FONT>        {8909899.0 / 18653125.0, 0.0, 0.0,<a name="line.104"></a>
<FONT color="green">105</FONT>         (-4521408.0 - 1137963.0 * FastMath.sqrt(6.0)) / 2937500.0,<a name="line.105"></a>
<FONT color="green">106</FONT>         (-4521408.0 + 1137963.0 * FastMath.sqrt(6.0)) / 2937500.0,<a name="line.106"></a>
<FONT color="green">107</FONT>         96663078.0 / 4553125.0, 2107245056.0 / 137915625.0,<a name="line.107"></a>
<FONT color="green">108</FONT>         -4913652016.0 / 147609375.0, -78894270.0 / 3880452869.0},<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>        // k11<a name="line.110"></a>
<FONT color="green">111</FONT>        {-20401265806.0 / 21769653311.0, 0.0, 0.0,<a name="line.111"></a>
<FONT color="green">112</FONT>         (354216.0 + 94326.0 * FastMath.sqrt(6.0)) / 112847.0,<a name="line.112"></a>
<FONT color="green">113</FONT>         (354216.0 - 94326.0 * FastMath.sqrt(6.0)) / 112847.0,<a name="line.113"></a>
<FONT color="green">114</FONT>         -43306765128.0 / 5313852383.0, -20866708358144.0 / 1126708119789.0,<a name="line.114"></a>
<FONT color="green">115</FONT>         14886003438020.0 / 654632330667.0, 35290686222309375.0 / 14152473387134411.0,<a name="line.115"></a>
<FONT color="green">116</FONT>         -1477884375.0 / 485066827.0},<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>        // k12<a name="line.118"></a>
<FONT color="green">119</FONT>        {39815761.0 / 17514443.0, 0.0, 0.0,<a name="line.119"></a>
<FONT color="green">120</FONT>         (-3457480.0 - 960905.0 * FastMath.sqrt(6.0)) / 551636.0,<a name="line.120"></a>
<FONT color="green">121</FONT>         (-3457480.0 + 960905.0 * FastMath.sqrt(6.0)) / 551636.0,<a name="line.121"></a>
<FONT color="green">122</FONT>         -844554132.0 / 47026969.0, 8444996352.0 / 302158619.0,<a name="line.122"></a>
<FONT color="green">123</FONT>         -2509602342.0 / 877790785.0, -28388795297996250.0 / 3199510091356783.0,<a name="line.123"></a>
<FONT color="green">124</FONT>         226716250.0 / 18341897.0, 1371316744.0 / 2131383595.0},<a name="line.124"></a>
<FONT color="green">125</FONT>    <a name="line.125"></a>
<FONT color="green">126</FONT>        // k13 should be for interpolation only, but since it is the same<a name="line.126"></a>
<FONT color="green">127</FONT>        // stage as the first evaluation of the next step, we perform it<a name="line.127"></a>
<FONT color="green">128</FONT>        // here at no cost by specifying this is an fsal method<a name="line.128"></a>
<FONT color="green">129</FONT>        {104257.0/1920240.0, 0.0, 0.0, 0.0, 0.0, 3399327.0/763840.0,<a name="line.129"></a>
<FONT color="green">130</FONT>         66578432.0/35198415.0, -1674902723.0/288716400.0,<a name="line.130"></a>
<FONT color="green">131</FONT>         54980371265625.0/176692375811392.0, -734375.0/4826304.0,<a name="line.131"></a>
<FONT color="green">132</FONT>         171414593.0/851261400.0, 137909.0/3084480.0}<a name="line.132"></a>
<FONT color="green">133</FONT>    <a name="line.133"></a>
<FONT color="green">134</FONT>      };<a name="line.134"></a>
<FONT color="green">135</FONT>    <a name="line.135"></a>
<FONT color="green">136</FONT>      /** Propagation weights Butcher array. */<a name="line.136"></a>
<FONT color="green">137</FONT>      private static final double[] STATIC_B = {<a name="line.137"></a>
<FONT color="green">138</FONT>          104257.0/1920240.0,<a name="line.138"></a>
<FONT color="green">139</FONT>          0.0,<a name="line.139"></a>
<FONT color="green">140</FONT>          0.0,<a name="line.140"></a>
<FONT color="green">141</FONT>          0.0,<a name="line.141"></a>
<FONT color="green">142</FONT>          0.0,<a name="line.142"></a>
<FONT color="green">143</FONT>          3399327.0/763840.0,<a name="line.143"></a>
<FONT color="green">144</FONT>          66578432.0/35198415.0,<a name="line.144"></a>
<FONT color="green">145</FONT>          -1674902723.0/288716400.0,<a name="line.145"></a>
<FONT color="green">146</FONT>          54980371265625.0/176692375811392.0,<a name="line.146"></a>
<FONT color="green">147</FONT>          -734375.0/4826304.0,<a name="line.147"></a>
<FONT color="green">148</FONT>          171414593.0/851261400.0,<a name="line.148"></a>
<FONT color="green">149</FONT>          137909.0/3084480.0,<a name="line.149"></a>
<FONT color="green">150</FONT>          0.0<a name="line.150"></a>
<FONT color="green">151</FONT>      };<a name="line.151"></a>
<FONT color="green">152</FONT>    <a name="line.152"></a>
<FONT color="green">153</FONT>      /** First error weights array, element 1. */<a name="line.153"></a>
<FONT color="green">154</FONT>      private static final double E1_01 =         116092271.0 / 8848465920.0;<a name="line.154"></a>
<FONT color="green">155</FONT>    <a name="line.155"></a>
<FONT color="green">156</FONT>      // elements 2 to 5 are zero, so they are neither stored nor used<a name="line.156"></a>
<FONT color="green">157</FONT>    <a name="line.157"></a>
<FONT color="green">158</FONT>      /** First error weights array, element 6. */<a name="line.158"></a>
<FONT color="green">159</FONT>      private static final double E1_06 =          -1871647.0 / 1527680.0;<a name="line.159"></a>
<FONT color="green">160</FONT>    <a name="line.160"></a>
<FONT color="green">161</FONT>      /** First error weights array, element 7. */<a name="line.161"></a>
<FONT color="green">162</FONT>      private static final double E1_07 =         -69799717.0 / 140793660.0;<a name="line.162"></a>
<FONT color="green">163</FONT>    <a name="line.163"></a>
<FONT color="green">164</FONT>      /** First error weights array, element 8. */<a name="line.164"></a>
<FONT color="green">165</FONT>      private static final double E1_08 =     1230164450203.0 / 739113984000.0;<a name="line.165"></a>
<FONT color="green">166</FONT>    <a name="line.166"></a>
<FONT color="green">167</FONT>      /** First error weights array, element 9. */<a name="line.167"></a>
<FONT color="green">168</FONT>      private static final double E1_09 = -1980813971228885.0 / 5654156025964544.0;<a name="line.168"></a>
<FONT color="green">169</FONT>    <a name="line.169"></a>
<FONT color="green">170</FONT>      /** First error weights array, element 10. */<a name="line.170"></a>
<FONT color="green">171</FONT>      private static final double E1_10 =         464500805.0 / 1389975552.0;<a name="line.171"></a>
<FONT color="green">172</FONT>    <a name="line.172"></a>
<FONT color="green">173</FONT>      /** First error weights array, element 11. */<a name="line.173"></a>
<FONT color="green">174</FONT>      private static final double E1_11 =     1606764981773.0 / 19613062656000.0;<a name="line.174"></a>
<FONT color="green">175</FONT>    <a name="line.175"></a>
<FONT color="green">176</FONT>      /** First error weights array, element 12. */<a name="line.176"></a>
<FONT color="green">177</FONT>      private static final double E1_12 =           -137909.0 / 6168960.0;<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>    <a name="line.179"></a>
<FONT color="green">180</FONT>      /** Second error weights array, element 1. */<a name="line.180"></a>
<FONT color="green">181</FONT>      private static final double E2_01 =           -364463.0 / 1920240.0;<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>      // elements 2 to 5 are zero, so they are neither stored nor used<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>      /** Second error weights array, element 6. */<a name="line.185"></a>
<FONT color="green">186</FONT>      private static final double E2_06 =           3399327.0 / 763840.0;<a name="line.186"></a>
<FONT color="green">187</FONT>    <a name="line.187"></a>
<FONT color="green">188</FONT>      /** Second error weights array, element 7. */<a name="line.188"></a>
<FONT color="green">189</FONT>      private static final double E2_07 =          66578432.0 / 35198415.0;<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>      /** Second error weights array, element 8. */<a name="line.191"></a>
<FONT color="green">192</FONT>      private static final double E2_08 =       -1674902723.0 / 288716400.0;<a name="line.192"></a>
<FONT color="green">193</FONT>    <a name="line.193"></a>
<FONT color="green">194</FONT>      /** Second error weights array, element 9. */<a name="line.194"></a>
<FONT color="green">195</FONT>      private static final double E2_09 =   -74684743568175.0 / 176692375811392.0;<a name="line.195"></a>
<FONT color="green">196</FONT>    <a name="line.196"></a>
<FONT color="green">197</FONT>      /** Second error weights array, element 10. */<a name="line.197"></a>
<FONT color="green">198</FONT>      private static final double E2_10 =           -734375.0 / 4826304.0;<a name="line.198"></a>
<FONT color="green">199</FONT>    <a name="line.199"></a>
<FONT color="green">200</FONT>      /** Second error weights array, element 11. */<a name="line.200"></a>
<FONT color="green">201</FONT>      private static final double E2_11 =         171414593.0 / 851261400.0;<a name="line.201"></a>
<FONT color="green">202</FONT>    <a name="line.202"></a>
<FONT color="green">203</FONT>      /** Second error weights array, element 12. */<a name="line.203"></a>
<FONT color="green">204</FONT>      private static final double E2_12 =             69869.0 / 3084480.0;<a name="line.204"></a>
<FONT color="green">205</FONT>    <a name="line.205"></a>
<FONT color="green">206</FONT>      /** Simple constructor.<a name="line.206"></a>
<FONT color="green">207</FONT>       * Build an eighth order Dormand-Prince integrator with the given step bounds<a name="line.207"></a>
<FONT color="green">208</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.208"></a>
<FONT color="green">209</FONT>       * integration), the last step can be smaller than this<a name="line.209"></a>
<FONT color="green">210</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.210"></a>
<FONT color="green">211</FONT>       * integration)<a name="line.211"></a>
<FONT color="green">212</FONT>       * @param scalAbsoluteTolerance allowed absolute error<a name="line.212"></a>
<FONT color="green">213</FONT>       * @param scalRelativeTolerance allowed relative error<a name="line.213"></a>
<FONT color="green">214</FONT>       */<a name="line.214"></a>
<FONT color="green">215</FONT>      public DormandPrince853Integrator(final double minStep, final double maxStep,<a name="line.215"></a>
<FONT color="green">216</FONT>                                        final double scalAbsoluteTolerance,<a name="line.216"></a>
<FONT color="green">217</FONT>                                        final double scalRelativeTolerance) {<a name="line.217"></a>
<FONT color="green">218</FONT>        super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,<a name="line.218"></a>
<FONT color="green">219</FONT>              new DormandPrince853StepInterpolator(),<a name="line.219"></a>
<FONT color="green">220</FONT>              minStep, maxStep, scalAbsoluteTolerance, scalRelativeTolerance);<a name="line.220"></a>
<FONT color="green">221</FONT>      }<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>      /** Simple constructor.<a name="line.223"></a>
<FONT color="green">224</FONT>       * Build an eighth order Dormand-Prince integrator with the given step bounds<a name="line.224"></a>
<FONT color="green">225</FONT>       * @param minStep minimal step (must be positive even for backward<a name="line.225"></a>
<FONT color="green">226</FONT>       * integration), the last step can be smaller than this<a name="line.226"></a>
<FONT color="green">227</FONT>       * @param maxStep maximal step (must be positive even for backward<a name="line.227"></a>
<FONT color="green">228</FONT>       * integration)<a name="line.228"></a>
<FONT color="green">229</FONT>       * @param vecAbsoluteTolerance allowed absolute error<a name="line.229"></a>
<FONT color="green">230</FONT>       * @param vecRelativeTolerance allowed relative error<a name="line.230"></a>
<FONT color="green">231</FONT>       */<a name="line.231"></a>
<FONT color="green">232</FONT>      public DormandPrince853Integrator(final double minStep, final double maxStep,<a name="line.232"></a>
<FONT color="green">233</FONT>                                        final double[] vecAbsoluteTolerance,<a name="line.233"></a>
<FONT color="green">234</FONT>                                        final double[] vecRelativeTolerance) {<a name="line.234"></a>
<FONT color="green">235</FONT>        super(METHOD_NAME, true, STATIC_C, STATIC_A, STATIC_B,<a name="line.235"></a>
<FONT color="green">236</FONT>              new DormandPrince853StepInterpolator(),<a name="line.236"></a>
<FONT color="green">237</FONT>              minStep, maxStep, vecAbsoluteTolerance, vecRelativeTolerance);<a name="line.237"></a>
<FONT color="green">238</FONT>      }<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>      /** {@inheritDoc} */<a name="line.240"></a>
<FONT color="green">241</FONT>      @Override<a name="line.241"></a>
<FONT color="green">242</FONT>      public int getOrder() {<a name="line.242"></a>
<FONT color="green">243</FONT>        return 8;<a name="line.243"></a>
<FONT color="green">244</FONT>      }<a name="line.244"></a>
<FONT color="green">245</FONT>    <a name="line.245"></a>
<FONT color="green">246</FONT>      /** {@inheritDoc} */<a name="line.246"></a>
<FONT color="green">247</FONT>      @Override<a name="line.247"></a>
<FONT color="green">248</FONT>      protected double estimateError(final double[][] yDotK,<a name="line.248"></a>
<FONT color="green">249</FONT>                                     final double[] y0, final double[] y1,<a name="line.249"></a>
<FONT color="green">250</FONT>                                     final double h) {<a name="line.250"></a>
<FONT color="green">251</FONT>        double error1 = 0;<a name="line.251"></a>
<FONT color="green">252</FONT>        double error2 = 0;<a name="line.252"></a>
<FONT color="green">253</FONT>    <a name="line.253"></a>
<FONT color="green">254</FONT>        for (int j = 0; j &lt; mainSetDimension; ++j) {<a name="line.254"></a>
<FONT color="green">255</FONT>          final double errSum1 = E1_01 * yDotK[0][j]  + E1_06 * yDotK[5][j] +<a name="line.255"></a>
<FONT color="green">256</FONT>                                 E1_07 * yDotK[6][j]  + E1_08 * yDotK[7][j] +<a name="line.256"></a>
<FONT color="green">257</FONT>                                 E1_09 * yDotK[8][j]  + E1_10 * yDotK[9][j] +<a name="line.257"></a>
<FONT color="green">258</FONT>                                 E1_11 * yDotK[10][j] + E1_12 * yDotK[11][j];<a name="line.258"></a>
<FONT color="green">259</FONT>          final double errSum2 = E2_01 * yDotK[0][j]  + E2_06 * yDotK[5][j] +<a name="line.259"></a>
<FONT color="green">260</FONT>                                 E2_07 * yDotK[6][j]  + E2_08 * yDotK[7][j] +<a name="line.260"></a>
<FONT color="green">261</FONT>                                 E2_09 * yDotK[8][j]  + E2_10 * yDotK[9][j] +<a name="line.261"></a>
<FONT color="green">262</FONT>                                 E2_11 * yDotK[10][j] + E2_12 * yDotK[11][j];<a name="line.262"></a>
<FONT color="green">263</FONT>    <a name="line.263"></a>
<FONT color="green">264</FONT>          final double yScale = FastMath.max(FastMath.abs(y0[j]), FastMath.abs(y1[j]));<a name="line.264"></a>
<FONT color="green">265</FONT>          final double tol = (vecAbsoluteTolerance == null) ?<a name="line.265"></a>
<FONT color="green">266</FONT>                             (scalAbsoluteTolerance + scalRelativeTolerance * yScale) :<a name="line.266"></a>
<FONT color="green">267</FONT>                             (vecAbsoluteTolerance[j] + vecRelativeTolerance[j] * yScale);<a name="line.267"></a>
<FONT color="green">268</FONT>          final double ratio1  = errSum1 / tol;<a name="line.268"></a>
<FONT color="green">269</FONT>          error1        += ratio1 * ratio1;<a name="line.269"></a>
<FONT color="green">270</FONT>          final double ratio2  = errSum2 / tol;<a name="line.270"></a>
<FONT color="green">271</FONT>          error2        += ratio2 * ratio2;<a name="line.271"></a>
<FONT color="green">272</FONT>        }<a name="line.272"></a>
<FONT color="green">273</FONT>    <a name="line.273"></a>
<FONT color="green">274</FONT>        double den = error1 + 0.01 * error2;<a name="line.274"></a>
<FONT color="green">275</FONT>        if (den &lt;= 0.0) {<a name="line.275"></a>
<FONT color="green">276</FONT>          den = 1.0;<a name="line.276"></a>
<FONT color="green">277</FONT>        }<a name="line.277"></a>
<FONT color="green">278</FONT>    <a name="line.278"></a>
<FONT color="green">279</FONT>        return FastMath.abs(h) * error1 / FastMath.sqrt(mainSetDimension * den);<a name="line.279"></a>
<FONT color="green">280</FONT>    <a name="line.280"></a>
<FONT color="green">281</FONT>      }<a name="line.281"></a>
<FONT color="green">282</FONT>    <a name="line.282"></a>
<FONT color="green">283</FONT>    }<a name="line.283"></a>




























































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